Cummings-Stell theory

In this section, we give a short summary of some of these theories and their applications, with an emphasis on contrasting the Pratt-Chandler, Cummings -Stell, and Wertheim approaches. The interested reader can find more technical details in the references. 

The interaction between ions of the same sign is assumed to be a pure hard sphere repulsion for r < a. It follows from simple steric considerations that an exact solution will predict dimerization only if i < a/2, but polymerization may occur for o/2 < L = o. However, an approximate solution may not reveal the fiill extent of polymerization that occurs in a more accurate or exact theory. Cummings and Stell [ ] used the model to study chemical association of uncharged atoms. It is closely related to the model for adliesive hard spheres studied by Baxter [70]. 

The behavior of assoeiating fluid near the hard wall was extensively studied in the framework of the theory diseussed above. The model of Cummings and Stell was applied to relatively dense fluids at a high degree of dimerization [33,36]. Fig. 1 presents the density profiles ealeulated within the framework of the eombined PYl/EMSA theory (i.e., the density profiles were evaluated from the PY 1 equation, whereas the bulk direet eorrelation fune-tions follow from the EMSA equation) and HNCl/EMSA approximations [33]. The ealeulations were performed for L = 0.42[Pg.181]

This point of interest is brought forward by the RISM approach to the structure of molecular liquids, and a RISM model with HNC closure supports a similar result for the excess chemical potential in terms of atom-atom correlations (Singer and Chandler, 1985 Hirata, 1998). RISM - reference interaction site model - is an acronym that refers to a class of theories for the joint two-atom distributions in molecular liquids. The most basic decision of RISM models is that theories of molecular liquids should focus first on the atom-atom distributions extracted from X-ray and neutron scattering data rather than more complex possibilities this highly practical point was not so obvious in an earlier epoch when models of molecular liquids were scarcely realistic on an atomic scale. That basic decision was encapsulated by invention of a site-site (or atom-atom) Ornstein-Zernike (SSOZ) (Cummings and Stell, 1982) equation that involved intramolecular atom-atom correlations. The original suggestions (Chandler and Andersen, 1972) were sufficiently successful as to support subsequent flamboyant developments, and to be substantially impervious to more fundamental improvements (Chandler et al, 1982). For these reasons a full discussion of the RISM models wouldn t fit here. Fortunately, a devoted exposition of current RISM work is already available (Hirata, 1998). 

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